Chapter 22 The Cost of Capital

LEARNING OBJECTIVES

1. Calculate cost of equity using dividend valuation model (DVM).2. Calculate dividend growth using the dividend growth model.3. Discuss the weaknesses of the DVM.4. Explain the relationship between systematic risk and return and describe the

assumptions and components of the capital asset price model (CAPM).5. Calculate the weighted average cost of capital (WACC) using book value and market

value weightings.6. Distinguish between average and marginal cost of capital.

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1. The Cost of Capital

1.1 Concept of cost of capital

1.1.1 Cost of Capital(a) The cost of capital is the rate of return that the enterprise must pay to

satisfy the providers of funds, and it reflects the riskiness of providing funds.

(b) The cost of capital is an opportunity cost of finance, because it is the minimum return that investors require. If they do not get this return, they will transfer some or all of their investment somewhere else. Here are two examples:(i) If a bank offers to lend money to a company, the interest rate it

charges is the yield that the bank wants to receive from investing in the company, because it can get just as good a return from lending the money to someone else. In other words, the interest rate is the opportunity cost of lending for the bank.

(ii) When shareholders invest in a company, the returns that they can expect must be sufficient to persuade them not to sell some or all of their shares and invest the money somewhere else. The yield on the shares is therefore the opportunity cost to the shareholders of not investing somewhere else.

1.1.2 The cost of capital has two aspects to it.(a) The cost of funds that a company raises and uses, and the return that investors

expect to be paid for putting funds into the company.(b) It is therefore the minimum return that a company should make on its own

investment, to earn the cash flows out of which investors can be paid their return.

1.1.3 The cost of capital can therefore be measured by studying the returns required by investors, and then used to derive a discount rate for DCF analysis and investment appraisal.

1.2 The risk-free rate of return (Rf)

1.2.1 The Rf is the minimum rate required by all investors for an investment whose

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returns are certain. It is given in questions as:(a) the return on Treasury bills or(b) the return on government gilts (英國公債).

1.2.2 Once funds have been advanced to a company, an investor faces the risk that they will not be returned. However some investments are less risky than others. For example lending to a government is considered to be extremely low risk as governments are always able to raise funds via taxation to pay back the investor.

1.2.3 The risk is so minimal that government securities are known as risk-free and the return they pay is a minimum benchmark against which all other investments can be measured.

1.2.4 The return is sometimes given in examination questions as the return on Treasury Bills or gilts (gilt-edged securities).(Gilt-edged securities (金邊證券) – 專指財政部代表政府發行的國家公債，由國家財政信譽作擔保，信譽度非常高。)

1.3 Return on risky investments – loan notes

1.3.1 Loan notes are lower risk investments than equities because the return is more predictable. This is because:(a) interest is a legal commitment(b) interest will be paid before any dividends(c) loans are often secured.

1.3.2 If a company issues loan notes, the returns needed to attract investors will therefore be:(a) higher than the Rf

(b) lower than the return on equities.1.3.3 Not all bonds have the same risk. There is a bond-rating system, which helps

investors distinguish a company’s credit risk. Below is the Fitch and Standard & Poor’s bond rating scales.

Fitch/S&P Grade RiskAAA Investment Highest qualityAA Investment High qualityA Investment StrongBBB Investment Medium gradeBB, B Junk SpeculativeCCC/CC/C Junk Highly speculative

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D Junk In default

1.3.4 If the company falls below a certain credit rating, its grade changes from investment quality to junk status. Junk bonds are aptly named: they are the debt of companies in some sort of financial difficulty. Because they are so risky they have to offer much higher yields than other debt. This brings up an important point: not all bonds are inherently safer than shares.

1.3.5 The minimum investment grade rating is BBB. Institutional investors may not like such a low rating. Indeed some will not invest below an A rating.

1.4 Return on risky investments – equities

1.4.1 Equity shareholders are paid only after all other commitments have been met. They are the last investors to be paid out of company profits.

1.4.2 As their earnings also fluctuate, equity shareholders therefore face the greatest risk of all investors. The level of risk depends on:(a) volatility of company earnings(b) extent of other binding financial commitments.

1.4.3 The return required to entice investors into risky securities can be shown as

Required return = Risk-free return + Risk premium

1.4.4 Since ordinary shares are the most risky investments the company offer, they are also the most expensive form of finance for the company.

2. Estimating the Cost of Equity – Dividend Valuation Model

2.1 Concept of cost of equity

2.1.1 The cost of equity finance to the company is the return the investors expect to achieve on their shares.

2.1.2 New funds from equity shareholders are obtained either from new issues of shares or from retained earnings. Both of these sources of funds have a cost.(a) Shareholders will not be prepared to provide funds for a new issue of shares

unless the return on their investment is sufficiently attractive.(b) Retained earnings also have cost. This is an opportunity cost, the dividend

forgone by shareholders.

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2.2 The dividend valuation model (DVM)

2.2.1 If we begin by ignoring share issue costs, the cost of equity, both for new issues and retained earnings, could be estimated by means of a dividend valuation model, on the assumption that the market value of shares is directly related to expected future dividends on the shares.

2.2.2 If the future dividend per share is expected to be constant in amount, then the ex dividend share price will be calculated by the formula:

So,

Where is the cost of equity capitalis the annual dividend per share, starting at year 1 and then continuing annually in perpetuity.is the ex-dividend share price

2.2.3 Example 1ABC Co has a dividend cover ratio of 4.0 times and expect zero growth in dividends. The company has one million $1 ordinary shares in issue and the market capitalization (value) of the company is $50 million. After-tax profits for next year are expected to be $20 million.

What is the cost of equity capital?

Solution:

Total dividends = 20 million/4 = $5 million.

= 5/50 = 10%

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2.3 The dividend growth model(Jun 09, Dec 12, Dec 13)

2.3.1 Shareholders will normally expect dividends to increase year by year and not to remain constant in perpetuity. The fundamental theory of share values states that the market price of a share is the present value of the discounted future cash flows of revenues from the share, so the market value given an expected constant growth in dividends would be:

Where is the current market price (ex div) is the current net dividend is the cost of equity capital

g is the expected annual growth in dividend paymentsand both and g are expressed as proportions.

It is often convenient to assume a constant expected dividend growth rate in perpetuity. The formula above then simplifies to:

Re-arrange this, we get a formula for the ordinary shareholders’ cost of capital.

or

2.3.2 Example 2A share has a current market value of 96c, and the last dividend was 12c. If the expected annual growth rate of dividends is 4%, calculate the cost of equity capital.

Solution:

Cost of capital

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2.4 Estimating the growth rate

(a) Extrapolating based on past dividend patterns

2.4.1 This method assumes that the past pattern of dividends is a fair indicator of the future.

2.4.2 Example 3Year Dividends Earnings

$ $2006 150,000 400,0002007 192,000 510,0002008 206,000 550,0002009 245,000 650,0002010 262,350 700,000

Dividends have risen from $150,000 in 2006 to $262,350 in 2010. The increase represents four years growth. (Check that you can see that there are four years growth, and not five years growth, in the table.)

The average growth rate, g, may be calculated as follows.150,000 x (1 + g)4 = 262,350

g = 0.15 or 15%

The growth rate over the last four years is assumed to be expected by shareholders into the indefinite future. If the company is financed by equity and there are 1,000,000 shares in issue, each with a market value of $3.35 ex div, the cost of equity, , is:

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(b) Earnings retention model (Gordon’s growth model)

2.4.3 This model assumes that the higher level of retentions in a business, the higher the potential growth rate. The formula is therefore:

g = bre

Where re = accounting rate of return or ROCE or ROIb = earnings retention rate

2.4.4 Example 4A company is about to pay an ordinary dividend of 16c a share. The share price is 200c. The accounting rate of return on equity is 12.5% and 20% of earnings are paid out as dividends.

Calculate the cost of equity for the company.

Solution:

b = 1 – dividend payout = 1 – 0.2 = 0.8g = r x b = 0.125 x 0.8 = 0.1P0 ex div = 200 – 16 = 184d0 = 16

2.4.5 Weaknesses of the dividend growth model(a) The model does not incorporate risk.

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(b) Dividend do not grow smoothly in reality so g is only an approximation.(c) The model fails to take capital gains into account, however it is argued that

a change of share ownership does not affect the present value of the dividend stream.

(d) No allowance is made for the effects of taxation although the model can be modified to incorporate tax.

(e) It assumes there are no issue costs for new shares.

3. Estimating the Cost of Equity – The Capital Asset Pricing Model (CAPM)

(Jun 13, Dec 14, Jun 15, Dec 15)3.1 The CAPM can be used to calculate a cost of equity and incorporates risk. The

CAPM is based on a comparison of the systematic risk of individual investments with the risks of all shares in the market.

3.2 The CAPM FormulaRequired return:

(Rj) = Rf + β(Rm - Rf)Where:Rj is the cost of equity capitalRf is the risk-free rate returnRm is the return from the market as a wholeβ is the beta factor of the individual security

3.3 Example 5Shares in ABC Co have a beta of 0.9. The expected returns to the market are 10% and the risk-free return is 4%. What is the cost of equity capital for ABC Co?

Solution:

Rj = Rf + β(Rm - Rf) = 4% + 0.9 x (10% – 4%) = 9.4%

3.4 Test your understanding 1Investors have an expected rate of return of 8% from ordinary shares in ABC Co, which have a beta of 1.2. The expected returns to the market are 7%.

What will be the expected rate of return from ordinary shares in BBC Co, which

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have a beta of 1.8?

Solution:

Question 1Yuen Long Manufacturing Ltd has been profitable for the past few years and currently holds $20 million cash. The board of directors is considering paying a cash dividend for the first time since the listing of the company on the Hong Kong Exchanges almost five years ago. The following is a set of information provided to the board of directors.

The company stock has a beta (β) value of 1.2, the expected return on the market portfolio is 12% and the risk-free rate is 5%.

The company is entirely equity financed. The company’s return on equity (ROE) will be 10% for the indefinite future. The corporate profits tax rate is 16%. Dividend income tax rate is 0%.

Required:

(a) Determine Yuen Long’s cost of equity. (5 marks)(b) Based on the information given in the question and your answers above, does it make

sense to pay the $20 million cash as dividends? Explain. (5 marks)(HKIAAT PBE Paper III Financial Management December 2003 Q3(a)

Question 2Look Right Company is considering expanding its retail business by adding a number of new stores in 2008. The total investment amount required is $100 million. Look Right currently does not have any long-term debt. It plans to finance the expansion with either bonds or new common stocks.

Look Right can sell $1,000 par value bonds at a net price of $1,050. The coupon interest rate is 9% paid annually, and the bonds will mature in 10 years. Look Right can also sell $1 par value common stocks at a net price of $25 per share. Dividend per share last year was $1 and is expected to have a perpetual annual growth rate of 10%. The corporate tax rate is

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17%.

Required:

(a) (i) Determine the after-tax cost of bonds. (4 marks)(ii) Determine the cost of common stock. (4 marks)(iii) Should “Look Right” choose bond financing or common stock financing which

has the lower cost based on the results in (i) and (ii)? Why?(4 marks)

(b) Explain the characteristics of bonds including their advantages and disadvantages from the point of view of the company. (8 marks)

(20 marks)(PBE Paper III Financial Management June 2007 Q2)

4. The Cost of Debt

4.1 Terminology

4.1.1 Types of debt:

4.1.2 Terminology(a) The term loan notes, bonds, loan stock and marketable debt, are used

interchangeably. Gilts are debts issued by the government.(b) Irredeemable debt – no repayment of principal – interest in perpetuity.(c) Redeemable debt – interest paid until redemption of principal.(d) Convertible debt – may be later converted to equity.(e) Vanilla bond (傳統債券，最普通的債券) – A bond with no unusual features,

paying a fixed rate of interest and redeemable in full on maturity. The term derives from vanilla or 'plain' flavoured ice-cream.

4.1.3 It should be noted that different types of debt have different costs. The cost of a loan note will not be the same as the cost of a bank loan.

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4.2 Irredeemable debt

4.2.1 FormulaCost of irredeemable debt capital, paying interest i in perpetuity, and having a current ex-interest price P0:

4.2.2 Example 6ABC Co has issued loan stock of $100 nominal value with annual interest of 9% per year, based on the nominal value. The current market price of the loan stock is $90. What is the cost of the loan stock?

Solution:

4.2.3 If interest on loan capital is paid other than annually,

Cost of loan capital =

Where n = number of times interest is paid per year

4.2.4 Example 7Henry has 12% irredeemable debentures in issue with a nominal value of $100. The market price is $95 ex interest. Calculate the cost of capital if interest is paid half-yearly.

Solution:

It interest is 12% annually, therefore 6% is payable half-yearly.

Cost of loan capital =

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4.3 Redeemable debt

4.3.1 If the debt is redeemable then in the year of redemption the interest payment will be received by the holder as well as the amount payable on redemption, so

Where Pn = the amount payable on redemption in year n.4.3.2 The above equation cannot be simplified, so “r” will have to be calculated by trial and

error, as an internal rate of return (IRR) or yield-to-maturity (YTM).

4.3.3 Example 8Owen has in issue 10% loan notes of a nominal value of $100. The market price is $90 ex interest. Calculate the cost of this capital if the debenture is:

(a) Irredeemable(b) Redeemable at par after 10 yearsIgnore taxation

Solution:

(a) The cost of irredeemable debt capital is

(b) The cost of redeemable debt capital. The capital profit that will be made from now to the date of redemption is $10 ($100 – $90). This profit will be made over a period of ten years which gives an annualized profit of $1 which is about 1% of current market value. The best trial and error figure to try first is therefore 12%.

Year Cash

flow ($)

DF

12%

PV

($)

DF

11%

PV

($)

0 Market value (90) 1.000 (90.00) 1.000 (90.00)

1 – 10 Interest 10 5.650 56.5 5.889 58.89

10 Capital payment 100 0.322 32.2 0.352 35.20

(1.30) 4.09

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The approximate cost of redeemable debt capital is, therefore:

Question 3The bonds of both Silicone Group Ltd and Pharmaceutical Corporation Ltd have one year to maturity and a par value of $1,000. Interest on the bonds is paid annually. Silicone Group’s bonds have an annual coupon rate of 8% and are selling at $1,043.48 each, while Pharmaceutical’s bonds are selling at $1,000 each. The two companies have the same credit ratings.

Required:

(a) What is the yield to maturity of Silicone Group’s bonds? What is the annual coupon rate on Pharmaceutical’s bonds? (6 marks)

(b) There are many factors that influence a company’s credit rating. Briefly discuss TWO of these factors. (4 marks)

(PBE Paper III Financial Management December 2004 Q5(a))

4.4 Debt capital and taxation

4.4.1 The interest on debt capital is likely to be an allowable deduction for purposes of taxation and so the cost of debt and the cost of share capital are not properly comparable costs. This tax relief on interest ought to be recognized in computations. The after-tax cost of irredeemable debt is:

4.4.2 Example 9A company has in issue 12% redeemable debt with 5 years to redemption. Redemption is at par. The current market value of the debt is $107.59. The corporate rate is 30%.

What is the cost of debt?

Solution:

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Year Cash

flow ($)

DF

10%

PV

($)

DF

5%

PV

($)

0 Market value (107.59) 1.000 (107.59) 1.000 (107.59)

1 – 5 Interest

[12 x (1 – 30%)]

8.4 3.791 31.84 4.329 36.36

5 Capital payment 100 0.621 62.1 0.784 78.4

(13.65) 7.17

The approximate cost of redeemable debt capital is, therefore:

Question 4Chen Porcelain Ltd is financed with both equity and debt, with a debt-to-equity ratio of 0.25. The company’s stock is listed on the Hong Kong Exchanges. The company’s 8% coupon outstanding bonds are traded at a discount with a yield-to-maturity of 9%. The company believes it can issue additional bonds with the same yield-to-maturity (9%). The market risk-premium is expected to be 8% and the risk-free rate is 2%. The corporate profit tax rate for Cheng Porcelain is 17%.

Required:

(a) The covariance between the returns on Cheng Porcelain and the market returns is 0.00169, the variance of returns on Cheng Porcelain is 0.004225 and the variance of the market returns is 0.001467. Determine the beta for Cheng Porcelain’s stock. (3 marks)

(b) What is the company’s after-tax cost of debt? (3 marks)(c) If Cheng Porcelain Ltd follows the “pecking order” in long-term financing patterns,

what would be its financing strategy? Briefly discuss. (4 marks)HKIAAT PBE Paper III Financial Management December 2003 Q4(a)

4.5 Convertible debt

4.5.1 Convertible bonds carry a rate of interest in the same way as vanilla bonds, but they also give the holder the right to exchange the bonds at some stage in the future into

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ordinary shares according to some prearranged formula.4.5.2 The owner of these bonds is not obliged to exercise this right of conversion and so

the bonds may continue until redemption as interest-bearing instruments.

4.5.3 Terminology(a) Floor value – market value without the conversion option.(b) Conversion ratio – this gives the number of ordinary shares into which a

convertible bond may be converted:

Conversion ratio =

(c) Conversion price – this gives the price of each ordinary share obtainable by exchange a convertible bond:

Conversion price =

(d) Conversion premium – this gives the difference between the conversion price and the market share price, expressed as a percentage:

Conversion premium =

(e) Conversion value – this is the value of a convertible bond if it were converted into ordinary shares at the current share price:Conversion value = Current share price x Conversion ratio

4.5.4 Example 10A company has issued $60 million 15-year 8.5% coupon bonds with a par value of $100. Each bond is convertible into 40 shares of the company ordinary shares, which are currently trading at $1.90.

Required:

(a) What is the conversion price?(b) What is the conversion premium?(c) What is the conversion value of the bond?

Solution:

(a) Conversion price = 100/40 = $2.50(b) Conversion premium = (2.50 – 1.90)/1.90 = 31.6%

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(c) Conversion value = $1.90 x 40 = $76

4.5.5 Test your understanding 2A company has issued convertible loan notes which are due to be redeemed at a 5% premium in five year’s time. The coupon rate is 8% and the current market value is $85. Instead of the redemption payment, the investor can choose to convert each loan note into 20 shares on the same date.

The company pays tax at 30% per annum.

The company’s shares are currently worth $4 and their value is expected to grow at a rate of 7% pa.

Find the cost of the convertible debt to the company.

Solution:

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4.6 Non-tradeable debt

4.6.1 Bank and other non-tradeable fixed interest loans simply need to be adjusted for tax relief:

Cost to the company = Interest rate × (1 – T) [T = tax rate]

4.6.2 Example 11A firm has a fixed rate bank loan of $1 million. It is charged 11% pa. The corporation tax rate is 30%.

What is the cost of the loan?

Solution:

Cost of the loan = 11% x (1 – 30%) = 7.7%

4.7 Preference shares

4.7.1 Although not strictly debt, the fixed rate of dividend and the fact that they are paid before ordinary shareholders, mean that preference shares are often treated as a form of lending similar to irredeemable debentures.

4.7.2 The main difference between preference shares and debt is that the preference dividend payments are not tax deductible. The formulae are therefore:

Where Dp = the constant annual preference dividendP0 = ex div market value of the share

4.7.3 Example 12

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A company has 50,000 8% preference shares in issue, nominal value $1. The current ex div market value is $1.20 per share.

What is the cost of the preference shares?

Solution:

4.8 Reasons of cost of equity greater than cost of debt(Dec 15)

4.8.1 Why the cost of equity is greater than the cost of debt?(a) Cost of equity is the return required by ordinary shareholders, in order to

compensate them for the risk associated with their equity investment.(b) If the risk of a company increases, its cost of equity also increases.(c) In liquidation, the debt holders must be paid off before any cash can be

distributed to ordinary shareholders. The risk faced by shareholders is therefore greater than the risk faced by debt holders, and the cost of equity is therefore greater than the cost of debt.

(d) Interest on debt finance must be paid before dividends can be paid to ordinary shareholders, so the risk faced by ordinary shareholders is greater than the risk faced by the debt holders.

5. Interest Rate Risk

5.1 Introduction

5.1.1 Many companies borrow, and if they do they have to choose between borrowing at a fixed rate of interest (usually by issuing bonds) or borrow at a floating (variable) rate (possibly through bank loans). There is some risk in deciding the balance or mix between floating rate and fixed rate debt. Too much fixed-rate debt creates an exposure to falling long-term interest rates and too much floating-rate debt creates an exposure to a rise in short-term interest rates.

5.2 The Causes of Interest Rate Fluctuations

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(a) The term structure of interest rates

5.2.1 The term structure of interest rate refers to the relationship between the long term interest rate and short term interest rate due to differences in inflation, maturity and interest rate risk. In drawing up the relationship, various premiums are added to reflect the risks involved. The terms structure is not a static structure and it is changing all the time.

5.2.1 There are several reasons why interest rates differ in different markets and market segments.(a) Risk – Higher risk borrowers must pay higher rates on their borrowing, to

compensate lenders for the greater risk involved.(b) The need to make a profit on re-lending – Financial intermediaries make

their profits from re-lending at a higher rate of interest than the cost of their borrowing.

(c) The size of the loan – Deposits above a certain amount with a bank or building society might attract higher rates of interest than smaller deposits.

(d) Different types of financial asset – Different types of financial asset attract different rates of interest. This is largely because of the competition for deposits between different types of financial institution.

(e) Government policy – The policy on interest rates might be significant too. A policy of keeping interest rates relatively high might therefore have the effect of forcing short-term interest rates higher than long-term rates.

(f) The duration of the lending – The term structure of interest rates refers to the way in which the yield on a security varies according to the term of the borrowing, that is the length of time until the debt will be repaid as shown by the yield curve. Normally, the longer the term of an asset to maturity, the higher the rate of interest paid on the asset.

(b) Yield curve (收益率曲線)

5.2.2 The yield curve is an analysis of the relationship between the yields on debt with different periods to maturity.

5.2.3 A yield curve can have any shape, and can fluctuate up and down for different maturities.

5.2.4 There are three main types of yield curve shapes: normal, inverted and flat (humped):(a) Normal yield curve – longer maturity bonds have a higher yield compared

with shorter-term bonds due to the risks associated with time.

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(b) Inverted yield curve – the short-term yields are higher than the longer-term yields, which can be a sign of upcoming recession.

(c) Flat (or humped) yield curve – the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition.

5.2.5 The slope of the yield curve is also seen as important: the greater the slope, the greater the gap between short- and long-term rates.

Inverted yield curve

5.2.6 The shape of the yield curve at any point in time is the result of the three following theories acting together:(a) Liquidity preference theory (流動性偏好理論)(b) Expectations theory(c) Market segmentation theory (市場分割理論)

5.2.7 Liquidity Preference, Expectations and Market Segmentation Theories

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(a) Liquidity preference theoryInvestors have a natural preference for more liquid (shorter maturity) investments. They will need to be compensated if they are deprived of cash for a longer period.

Therefore the longer the maturity period, the higher the yield required leading to an upward sloping curve, assuming that the interest rates were not expected to fall in the future.

(b) Expectations theoryThis theory states that the shape of the yield curve varies according to investors' expectations of future interest rates. A curve that rises steeply from left to right indicates that rates of interest are expected to rise in the future. There is more demand for short-term securities than long-term securities since investors' expectation is that they will be able to secure higher interest rates in the future so there is no point in buying long-term assets now. The price of short-term assets will be bid up, the price of long-term assets will fall, so the yields on short-term and long-term assets will consequently fall and rise.

(c) Market segmentation theoryThe market segmentation theory suggests that there are different players in the short-term end of the market and the long-term end of the market. As a result the two ends of the curve may have different shapes, as they are influenced independently by different factors.

The result is separate yield curves that probably do not meet very smoothly. This introduces a ‘kink’ to the yield curve presumably determined by arbitrage between the different markets to gain risk-free return.

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5.2.8 Significance of Yield Curves to Financial ManagersFinancial managers should inspect the current shape of the yield curve when deciding on the term of borrowings or deposits, since the curve encapsulates the market's expectations of future movements in interest rates.

A corporate treasurer might analyse a yield curve to decide for how long to borrow. For example, suppose a company wants to borrow $20 million for five years and would prefer to issue bonds at a fixed rate of interest. One option would be to issue bonds with a five-year maturity. Another option might be to borrow short-term for one year, say, in the expectation that interest rates will fall, and then issue a four-year bond. When borrowing large amounts of capital, a small difference in the interest rate can have a significant effect on profit. For example, if a company borrowed $20 million, a difference of just 25 basis points (0.25% or one quarter of one per cent) would mean a difference of $50,000 each year in interest costs. So if the yield curve indicates that interest rates are expected to fall then short-term borrowing for a year, followed by a 4-year bond might be the cheapest option.

Question 5 (20 marks – approximately 36 minutes)You are in charge of the Treasury Department of a Multinational Corporation. One day, you read the Stock Exchange Journal and find the following table showing the yield rate of

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different maturity of US Treasury Bills.

Maturity Yield (%) Yesterday Last week Last month3 month 0.16 0.16 0.16 0.156 month 0.25 0.25 0.26 0.322 year 1.16 1.07 0.94 1.103 year 1.68 1.63 1.47 1.605 year 2.63 2.59 2.39 2.5210 year 3.66 3.68 3.54 3.4830 year 4.51 4.54 4.45 4.28

Required:

(a) Sketch a yield curve according to the information given in the above table.(4 marks)

(b) Based on the answer in (a), is it a normal yield curve? Explain the expected economic conditions of this curve. (3 marks)

(c) Sketch an inverted yield curve. (2 marks)(d) Explain the “term structure of interest rate”. Is it static? (4 marks)(e) Explain the behavior in borrowing terms when management observes a steeply

upward sloping yield curve. (4 marks)(f) What are the main differences between Capital Market and Money Market?

(3 marks)(PBE Paper III Management Accounting and Finance December 2010 Q3)

6. The Weighted Average Cost of Capital (WACC)(Jun 09, Dec 09, Dec 10, Jun 13, Dec 13, Dec 14, Jun 15, Dec 15)

6.1 In the analysis so far carried out, each source of finance has been examined in isolation. However, the practical business situation is that there is a continuous raising of funds from various sources.

6.2 These funds are used, partly in existing operations and partly to finance new projects. These is not normally any separation between funds from different sources and their application to specific projects:

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6.3 Even if a question tells you that a project is to be financed by the raising of a particular loan or through an issue of shares, in practice the funds raised will still be added to the firm’s pool of funds and it is from that pool that the project will be funded.

6.4 It is therefore not the marginal cost of the additional finance, but the overall average cost of all finance raised, that is required for project appraisal.

6.5 The general approach is to calculate the cost of each individual source of medium-long term finance and then weight it according to its importance in the financing mix.

6.6 WACC(a) Weighted average cost of capital is the average cost of the company’s finance

(equity, debentures, bank loans) weighted according to the proportion each element bears to the total pool of capital.

(b) A general formula for the WACC is as follows.

Where ke = the cost of equitykd = the cost of debtVe = the market value of equity in the firmVd = the market value of debt in the firmT = the rate of company tax

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(c) To find an average cost, the various sources of finance must be weighted according to the amount of each held by the company. The weights for the sources of finance could be: Book values – represents historic cost of finance. Market values – represent current opportunity cost of finance.

Wherever possible market value should be used because book values based on historical costs and their use will seriously understate the impact of the cost of equity finance. If the WACC is underestimated, unprofitable projects will be accepted.

6.7 Example 13A entity has the following information in its statement of financial position.

$000Ordinary shares of 50c 2,50012% unsecured loan notes 1,000

The ordinary shares are currently quoted at 130c each and the loan notes are trading at $72 per $100 nominal. The ordinary dividend of 15c has just been paid with an expected growth rate of 10%. Corporation tax is currently 30%.

Calculate the WACC for this entity.

Solution:

Market values:$000

Equity (Ve): 2,500/0.5 x 1.30 6,500Loan notes (Vd): 1,000 x 0.72 720

7,220

Cost of equity:

Cost of loan stock:

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6.8 When WACC is suitable for using as discount rate in investment appraisal?(Jun 11, Jun 13)

(a) When the risk of the investment project is similar to the current risks of the investing company

(b) From the point of view of business risk:(i) Similar to the business risk of existing operations(ii) If not, a project specific discount rate should be considered(iii) CAPM should be applied under this situation

(c) From the point of view of financial risk:(i) Similar to the financial risk of existing operations(ii) If not, adjusted present value (APV) or the CAPM-derived project

specific cost of capital can be adjusted to reflect the financial risk of the project.

(d) Other factors to consider:(i) Project size compares with the size of the company – it should be

small in relation to the size of the existing business.(e) If one of the above factors is not similar, WACC should not be applied.

Question 6What is the general method used to determine the required rate of return in project evaluation? Explain by using a suitable formula. (5 marks)

(HKIAAT PBE Paper II Management Accounting and Finance December 2010 Q1(f))

Question 7AAT Co. Ltd has the following extracts from its statement of financial position:

$Long term liabilityBond payable (face value = $1,000) 10,000,000

EquityCommon stock (par = $1) 250,000

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Stock premium 1,000,000Retained earnings 5,000,000

6,250,000

The market price of the stock is $40 per share. AAT is expected to pay an annual dividend in the amount of $2.0 per share. The dividend growth rate is 3%. The bonds carry a 6% coupon, pay interest annually, and mature in 4.641 years. The bonds are selling at 102% of face value. The yield rate of similar types of bond is 5.5%. The tax rate is 15%.

You are a financial analyst of AAT Co Ltd. The Finance Director has asked you to calculate the Weighted Average Cost of Capital (WACC) of the company and then add a 2% premium to the figure you calculated as a discount rate in evaluating the project.

Required:

(a) What is the market value of the common stock? (2 marks)(b) What is the market value of the bonds? (2 marks)(c) What is the cost of equity? (5 marks)(d) What is the before-tax cost of debt? (2 marks)(e) What is the weighted average cost of capital (WACC)? (5 marks)(f) Why is a premium percentage of, say 2%, often added to the WACC when it is used

as a discount rate in evaluating the project? (4 marks)(HKIAAT PBE Paper II Management Accounting and Finance June 2009 Q5)

Question 8(a) The financial manager of the FED Company presents the following two alternatives

to raise funds:

Alternative 1: Borrow from a bank at an annual interest rate of 9%, interest to be paid every six months.

Alternative 2: Issue new common stock with $1 par value per share, $15 market price per share, $1.2 dividend per share paid last year with an expected annual growth rate of 10% and a flotation cost of 5% of the market price.

FED has a corporate tax rate of 17% and a debt/equity ratio of 50/50.

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Required:

(i) Determine the after tax annual effective cost of borrowing from the bank.4 marks)

(ii) Determine the after tax annual effective cost of issuing new common stock.(4 marks)

(b) The financial manager continues to present, “We need to calculate the weighted average cost of capital (WACC) of our company for two purposes. The WACC will help us determine not only what projects we should invest in, but also what sources of financing we should tap.”

Required:

(i) Determine WACC using the information in (a). (4 marks)(ii) Discuss how WACC could help a company make investment decisions.

(4 marks)(iii) Discuss how WACC could help a company make financing decisions.

(4 marks)(PBE Paper III Financial Management December 2007 Q2)

Question 9Forever company has 80,000 bonds outstanding with face value $1,000 that are selling at par value. Bonds with similar characteristics are yielding 8.5%. The company also has 4 million shares of common stock outstanding. The stock has a beta of 1.1 and sells for $40 per share. The government treasury bill is yielding 4% and the market risk premium is 8%. Corporate tax rate is 10%.

Required:

(a) (i) Calculate the after-tax cost of debt. (2 marks)(ii) Calculate the cost of common stock. (3 marks)

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(iii) Calculate the WACC of Forever Company. (7 marks)(b) Suggest THREE reasons why investors usually prefer firms issuing bonds rather

than issuing shares. (6 marks)(c) What do you observe in the stock price on its ex-dividend date? (2 marks)

(PBE Paper III Financial Management June 2008 Q1)

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7. Marginal Cost of Capital (MCC)

7.1 MCCMCC is the cost associated with raising one additional dollar of capital.

It can be argued that the current weighted average cost of capital should be used to evaluate projects. Where a company’s capital structure changes only very slowly over time, the marginal cost of new capital should be roughly equal to the weighted average cost of current capital.

Where gearing levels fluctuate significantly, or the finance for new project carries a significantly different level of risks to that of the existing company, there is good reason to seek an alternative marginal cost of capital.

7.2 Example 14A company has the following capital structure:

After tax cost Market value After tax cost × Market value

Source % $mEquity 12 10 1.2Preference 10 2 0.2Loan notes 7.5 8 0.6

20 2.0

WACC =

The company’s directors have decided to embark on major capital expenditure, which will be financed by a major issue of funds. The estimated project cost is $3,000,000, 1/3 of which will be financed by equity, 2/3 of which will be financed by loan notes. As a result of undertaking the project, the cost of equity (existing and new shares) will rise from 12% to 14%. The cost of preference shares and the cost of existing loan notes will remain the same, while the after tax cost of the new loan notes will be 9%.

Required:

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Calculate the company’s new WACC, and its marginal cost of capital.

Solution:

New WACCAfter tax cost Market value After tax cost ×

Market valueSource % $mEquity 14 11 1.54Preference 10 2 0.2Existing loan notes 7.5 8 0.60New loan notes 9 2 0.18

23 2.52

WACC =

MCC =

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Additional Examination Style Questions

Question 10Burse Co wishes to calculate its weighted average cost of capital and the following information relates to the company at the current time:

Number of ordinary shares 20 millionBook value of 7% convertible debt $29 millionBook value of 8% bank loan $2 millionMarket price of ordinary shares $5.50 per shareMarket value of convertible debt $107.11 per $100 bondEquity beta of Burse Co 1.2Risk-free rate of return 4.7%Equity risk premium 6.5%Rate of taxation 30%

Burse Co expects share prices to rise in the future at an average rate of 6% per year. The convertible debt can be redeemed at par in eight years’ time, or converted in six years’ time into 15 shares of Burse Co per $100 bond.

Required:

(a) Calculate the market value weighted average cost of capital of Burse Co. State clearly any assumptions that you make. (12 marks)

(b) Discuss the circumstances under which the weighted average cost of capital can be used in investment appraisal. (6 marks)

(c) Discuss whether the dividend growth model or the capital asset pricing model offers the better estimate of the cost of equity of a company. (7 marks)

(Total 25 marks)(ACCA F9 Financial Management June 2008 Q1)

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Question 11Rupab Co is a manufacturing company that wishes to evaluate an investment in new production machinery. The machinery would enable the company to satisfy increasing demand for existing products and the investment is not expected to lead to any change in the existing level of business risk of Rupab Co.

The machinery will cost $2.5 million, payable at the start of the first year of operation, and is not expected to have any scrap value. Annual before-tax net cash flows of $680,000 per year would be generated by the investment in each of the five years of its expected operating life. These net cash inflows are before taking account of expected inflation of 3% per year. Initial investment of $240,000 in working capital would also be required, followed by incremental annual investment to maintain the purchasing power of working capital.

Rupab Co has in issue five million shares with a market value of $3.81 per share. The equity beta of the company is 1.2. The yield on short-term government debt is 4.5% per year and the equity risk premium is approximately 5% per year.

The debt finance of Rupab Co consists of bonds with a total book value of $2 million. These bonds pay annual interest before tax of 7%. The par value and market value of each bond is $100.

Rupab Co pays taxation one year in arrears at an annual rate of 25%. Capital allowances (tax-allowable depreciation) on machinery are on a straight-line basis over the life of the asset.

Required:

(a) Calculate the after-tax weighted average cost of capital of Rupab Co. (6 marks)(b) Prepare a forecast of the annual after-tax cash flows of the investment in nominal terms,

and calculate and comment on its net present value. (8 marks)(c) Explain how the capital asset pricing model can be used to calculate a project-specific

discount rate and discuss the limitations of using the capital asset pricing model in investment appraisal. (11 marks)

(Total 25 marks)(ACCA F9 Financial Management December 2008 Q3)

Question 12

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CAP is a listed company that owns and operates a large number of farms throughout the world. A variety of crops are grown.

Financing structureThe following is an extract from the balance sheet of CAP at 31 March 2010.

$mOrdinary shares of $1 each 200Reserves 1009% irredeemable $1 preference shares 508% loan stock 2011 250

600

The ordinary shares were quoted at $3 per share ex div on 31 March 2010. The beta of CAP’s equity shares is 0.8, the annual yield on treasury bills is 5%, and financial markets expect an average annual return of 15% on the market index.

The market price per preference share was $0.90 ex div on 31 March 2010.

Lock stock interest is paid annually in arrears and is allowable for tax at a tax rate of 30%. The loan stock was priced at $100.57 ex interest per $100 nominal on 31 March 2010. The loan stock is redeemable on 31 March 2011.

Assume that taxation is payable at the end of the year in which taxable profits arise.

A new projectDifficult trading conditions in US farming have caused CAP to decide to convert a number of its farms in Southern American into camping sites with effect from the 2011 holiday season. Providing the necessary facilities fro campers will require major investment, and this will be financed by a new issue of loan stock. The returns on the new campsite business are likely to have a very low correlation with those of the existing farming business.

Required:

(a) Using the capital asset pricing model, calculate the required rate of return on equity of CAP at 31 March 2010. Ignore any impact from the new campsite project. Briefly explain the implications of a Beta of less than 1, such as that for CAP. (4 marks)

(b) Calculate the weighted average cost of capital of CAP at 31 March 2010 (use your

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calculation in answer to requirement (a) above for the cost of equity). Ignore any impact from the new campsite project. (10 marks)

(c) Without further calculations, identify and explain the factors that may change CAP’s equity beta during the year ending 31 March 2011. (5 marks)

(d) Explain the limitations of the capital asset pricing model. (6 marks)(Total 25 marks)

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